Several examples with detailed solutions and exercises with answers on addition of
fractions, are presented.
_{}
is used here to denote the fraction of a over b. a is called the numerator and b is called the denominator and must be non zero.
Examples of fractions: _{}
NOTE:
_{}
is undefined since division by zero is undefined in mathematics.
A calculator to add fractions is included in this website. You may use it to check your answers.
How to add fractions?
1. Add fractions with equal denominator
Example 1: Add and simplfy.
Solution to Example 1
To add fractions with the same denominator, you add the numerators, keep the same denominator and simplify if possible
Example 2: Add, simplify and express the final answer as a fraction.
Solution to Example 2
Add the numerators
2. Add fractions with non equal denominators
Example 3: Add, simplify and express the final answer as a fraction.
Solution to Example 3
We first need to find the lowest common multiple (LCM) of the denominators 9 and 6 by factoring into prime factors.
We next convert the two given fractions so that they have common denominator equal to the LCM = 18. The denominator of the fraction _{} is 9 and we need to multiply numerator and denominator by 2 in order to change the denominator to 18
The denominator of the fraction _{} is 6 and we need to multiply numerator and denominator by 3 in order to change the denominator to 18
Now that we have converted the two fractions so that they have common denominator, we can easily add them as follows
Example 4: Add, simplify and express the final answer as a fraction and as a mixed number.
Solution to Example 4
Find the LCM of the denominators 15 and 55
We convert the given fractions so the they have common denominator equal to the LCM = 165. The denominator of the fraction
_{} is 15 and both numerator and denominator need to be multiplied by 11 in order to change the denominator to 165
The second fraction _{} is converted to one with the denominator equal to 165 by multiplying numerator and denominator by 3 in order to change the denominator to 165
We now add the fractions
Example 5: Add, simplify and express the final answer as a fraction.
Solution to Example 5
We first convert 2 into a fraction
The common denominator will be 5
We now add
Exercises: Add, simplify and express the answer as a fraction and as a mixed number.
Answers to Above Exercises:.
More on fractions
and fraction calculators.
